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Simplifying 4x + 12 + 3 = (2x + -3)(2x + 3) Reorder the terms: 12 + 3 + 4x = (2x + -3)(2x + 3) Combine like terms: 12 + 3 = 15 15 + 4x = (2x + -3)(2x + 3) Reorder the terms: 15 + 4x = (-3 + 2x)(2x + 3) Reorder the terms: 15 + 4x = (-3 + 2x)(3 + 2x) Multiply (-3 + 2x) * (3 + 2x) 15 + 4x = (-3(3 + 2x) + 2x * (3 + 2x)) 15 + 4x = ((3 * -3 + 2x * -3) + 2x * (3 + 2x)) 15 + 4x = ((-9 + -6x) + 2x * (3 + 2x)) 15 + 4x = (-9 + -6x + (3 * 2x + 2x * 2x)) 15 + 4x = (-9 + -6x + (6x + 4x2)) Combine like terms: -6x + 6x = 0 15 + 4x = (-9 + 0 + 4x2) 15 + 4x = (-9 + 4x2) Solving 15 + 4x = -9 + 4x2 Solving for variable 'x'. Reorder the terms: 15 + 9 + 4x + -4x2 = -9 + 4x2 + 9 + -4x2 Combine like terms: 15 + 9 = 24 24 + 4x + -4x2 = -9 + 4x2 + 9 + -4x2 Reorder the terms: 24 + 4x + -4x2 = -9 + 9 + 4x2 + -4x2 Combine like terms: -9 + 9 = 0 24 + 4x + -4x2 = 0 + 4x2 + -4x2 24 + 4x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 24 + 4x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(6 + x + -1x2) = 0 Factor a trinomial. 4((3 + -1x)(2 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {3, -2}
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